Intrinsic Mode Functions Research Articles

Wavelet transform-based mode decomposition for EEG signals under general anesthesia

Background Mode decomposition methods are used to extract the characteristic intrinsic mode function (IMF) from various multidimensional time series signals. We analyzed an electroencephalogram (EEG) dataset for sevoflurane anesthesia using two wavelet transform-based mode decomposition methods, comprising the empirical wavelet transform (EWT) and wavelet mode decomposition (WMD) methods, and compared the results with those from the previously reported variational mode decomposition (VMD) method. Methods To acquire the EEG data, we used the software application EEG Analyzer, which enabled the recording of raw EEG signals via the serial interface of a bispectral index (BIS) monitor. We also created EEG mode decomposition software to perform empirical mode decomposition (EMD), VMD, EWT, and WMD operations. Results When decomposed into six IMFs, the EWT enables narrow band separation of the low-frequency bands IMF-1 to IMF-3, in which all central frequencies are less than 10 Hz. However, in the upper IMF of the high-frequency band, which has a center frequency of ≥ 10 Hz, the dispersion within the frequency band covered was widespread among the individual patients. In WMD, a narrow band of clinical interest is specified using a bandpass filter in a Meyer wavelet filter bank within a specific mode-decomposition discipline. When compared with the VMD and EWT methods, the IMF that was decomposed via WMD was accommodated in a narrow band with only a small variance for each patient. Multiple linear regression analyses demonstrated that the frequency characteristics of the IMFs obtained from WMD best tracked the changes in the BIS upon emergence from general anesthesia. Conclusions The WMD can be used to extract subtle frequency characteristics of EEGs that have been affected by general anesthesia, thus potentially providing better parameters for use in assessing the depth of general anesthesia.

DGTNet：dynamic graph attention transformer network for traffic flow forecasting

Abstract Graph-based traffic flow prediction plays a crucial role in urban traffic management and planning. In this paper, we propose a novel Dynamic Graph Attention Transformer Network (DGTnet), which is designed to address the issue of inadequately integrating of temporal and spatial dimensions in traditional models. DGTnet maintains temporal continuity while revealing the complex dynamic relationships between key nodes in the urban traffic system, capturing the periodic changes in the rhythm of city life. Specifically, this study adopts adaptive signal decomposition technology to decompose traffic data into multiple intrinsic mode functions (IMFs), effectively capturing the dynamic changes in traffic flow. This decomposition method is key to the implementation of DGTnet dynamic graph construction, enabling the analysis of traffic flow at different time scales, thereby providing a new perspective for traffic flow prediction research. In the traffic prediction module, we comprehensively consider node, edge, and graph structural information, adopting a multi-head self-attention mechanism to achieve direct cross-modeling in both temporal and spatial dimensions. Finally, we introduce a position-wise feed forward network layer to integrate different types of data and capture nonlinear relationships. The experimental results, based on the public transportation network data sets METR_LA, PEMS_BAY, PEMS03 and PEMS07, demonstrate that DGTNet exhibits notable enhancements in three evaluation indicators, namely the Mean Absolute Percentage Error (MAPE), the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The pertinent code has been made available for public access at https://github.com/chenjing0616/DGTNet.

Analysis of Cardiovascular Disease Classification Through Deep Learning Approach

Multiple cardiovascular disease classification from Electrocardiogram (ECG) signal is necessary for efficient and fast remedial treatment of the patient. This paper presents a method to classify multiple heart diseases using one dimensional deep convolutional neural network (CNN) where a modified ECG signal is given as an input signal to the network. Each ECG signal is first decomposed through Empirical Mode Decomposition (EMD) and higher order Intrinsic Mode Functions (IMFs) is combined to form a modified ECG signal. It is believed that the use of EMD would provide a broader range of information and can provide denoising performance. This processed signal is fed into the CNN architecture that classifies the record according to cardiovascular diseases using soft max regress or at the end of the network. It is observed that the CNN architecture learns the inherent features of the modified ECG signal better in comparison with the raw ECG signal. The method is applied on three publicly available ECG databases and it is found to be superior to other approaches in terms of classification accuracy. In MIT-BIH, St. Petersburg, PTB databases the proposed method achieves maximum accuracy of 0.9770, 0.9971 and 0.9871 respectively.

Damage detection for railway bridges using time‐frequency decomposition and conditional generative model

AbstractA novel damage detection model, which utilizes the spatiotemporal characteristics of the acceleration data, is proposed to assess the structural integrity of railway bridges. For this, the measured acceleration data are decomposed into several intrinsic mode functions (IMFs) using the sparse random mode decomposition model. The generated IMFs are subsequently integrated into the enhanced time series conditional generative adversarial network model to identify possible damage in bridges across various frequency bands. The influence of environmental and operational variables (EOVs), particularly temperature fluctuations, was also investigated. The proposed model was verified using both numerical and experimental data from a plate girder bridge. Further validation was conducted using the Z24 bridge dataset, and damage cases under the influence of EOVs were successfully predicted. Throughout the validation process, various anomaly metrics were introduced to establish a threshold value, and a covariance‐based time domain metric was proven to be the most effective in our cases.

Integrated Method of Future Capacity and RUL Prediction for Lithium‐Ion Batteries Based on CEEMD‐Transformer‐LSTM Model

ABSTRACTAccurately predict the remaining useful life (RUL) of lithium‐ion batteries for energy storage is of critical significance to ensure the safety and reliability of electric vehicles, which can offer efficient early warning signals in a timely manner. Considering nonlinear changes in the aging trajectory of lithium‐ion batteries, a method for predicting the RUL of lithium‐ion batteries was proposed in this study based on a complementary ensemble empirical mode decomposition (CEEMD) as well as transformer and long short‐term memory (LSTM) neural network dual‐drive machine learning model. First, the CEEMD algorithm was adopted to decompose the raw aging data of lithium‐ion batteries into intrinsic mode function (IMF) sequences and residual sequence, where the number of modal layers was produced by the proposed posterior feedback entropy and relevance (PFER) method. Second, prediction models of LSTM and transformer neural networks were established to predict IMF and residual sequences. Simultaneously, the sparrow search algorithm (SSA) was used to obtain the optimal value of the hyperparameter learning rate for the RUL prediction model. Finally, the predicted IMF and residual sequences were combined to comprehensively calculate the future lifespan aging trajectory of lithium‐ion batteries. The aging data of two groups of lithium‐ion batteries were obtained from the CALCE at the University of Maryland as well as the laboratory at AQNU University to verify the proposed method. Experimental results demonstrated that the proposed method can effectively predict the RUL of lithium‐ion batteries; moreover, it exhibited better robustness and generalization ability.

A novel epilepsy detection approach using intrinsic multiscale entropy analysis and DSEAM-enhanced 1D-ResNets

Abstract Epilepsy, a prevalent neurological disorder, typically requires a complex diagnostic process involving medical history inquiry, physical examination, head computed tomography, and electroencephalogram (EEG) visual examination. Among the existing epilepsy automated detection algorithms, machine learning methods require manual feature selection. Most of deep learning algorithms for automatic detection have high complexity and computational complexity. To address this issue, this study proposes a high-precision, robust, and low computational epilepsy automatic detection algorithm based on EEG signal processing. The study utilizes ensemble empirical mode decomposition to preprocess the original EEG signal, breaking it down into intrinsic mode functions (IMFs) across various frequency bands. These IMFs contain information about epilepsy occurrence within the signal at different frequency bands. To enhance computational efficiency and reduce data dimension, the refined composite multiscale dispersion entropy of each IMF is further computed at different scales, referred to as intrinsic multiscale entropy (IME) analysis. IME analysis consolidates epilepsy occurrence information from EEG signals across different frequency bands and scales, linking entropy values to generate feature vectors. Drawing inspiration from successful deep residual networks and Squeeze-and-Excitation networks, the study introduces a double Squeeze-and-Excitation attention module enhanced one-dimensional residual network to classify one-dimensional feature vectors. The proposed method was tested on epilepsy dataset from University of Bonn, and the results demonstrated superior classification performance. In the experiment, the distinction between normal and epileptic EEG signals achieved 100% accuracy rate, while distinguishing between normal, epileptic interval, and epileptic EEG signals achieved accuracy rate of 99.41%.

Predictive combination model for CH4 separation and CO2 sequestration with CO2 injection into coal seams: VMD-STA-BiLSTM-ELM hybrid neural network modeling

In the experimental process of separating coal seam gas using the CO2 displacement method, establishing a predictive model for key variables is essential to optimize displacement parameters, increase coal seam gas recovery, and improve CO2 sequestration efficiency. Traditional modeling methods often struggle with the complex nature of industrial data and are susceptible to overfitting due to multicollinearity caused by long-term datasets. This paper presents a hybrid predictive model based on variational mode decomposition (VMD), a spatiotemporal attention mechanism (STA), a bidirectional long short-term memory network (BiLSTM), and an extreme learning machine (ELM). During the offline phase, VMD is used to decompose raw data into intrinsic mode functions (IMFs). The hidden state from the last time step of the STA-BiLSTM is then added to the original data to enrich the features for ELM training. In the online prediction phase, the outputs from the VMD-STA-BiLSTM and VMD-STA-BiLSTM-ELM models are combined using an error reciprocal method to generate the final prediction. The proposed model is validated with experimental datasets from CO2 displacement for coal seam CH4 under various conditions, as well as with N2-ECBM and CO2-ECBM engineering datasets. The results show that the hybrid model surpasses VMD-ELM, STA-BiLSTM-ELM, BiLSTM, STA-BiLSTM, ELM, TCN, and Attention-TCN models in predictive accuracy. Even in multi-step and rolling predictions, the model exhibits minimal impact from cumulative errors, maintaining accurate forecasts with strong generalization and robustness. It effectively captures feature patterns across different datasets and accurately predicts unknown data. The model shows potential for application in diverse scenarios and complex environments, offering reliable support and decision-making for the field application of CO2 displacement in coal seam CH4 separation. It is an effective and promising predictive approach to enhance coal seam gas recovery and CO2 sequestration efficiency.

Fault diagnosis of wind turbine gears based on OCSSA-VMD and WOA-CNN-BiLSTM

Abstract The accuracy of wind turbine gearbox fault diagnosis will be compromised if the fault feature data is not adequately extracted during operation. To enhance fault identification efficiency and mitigate human interference in parameter setting, this paper introduces an optimized mode decomposition algorithm OCSSA-VMD, derived from variational mode decomposition (VMD) and further optimized by osprey-Cauchy-sparrow search algorithm (OCSSA). This algorithm offers two key advantages: (1) automatic optimization of parameters such as the number of modes k and penalty factor α; (2) reduction of feature dimensionality through mean impact value (MIV) algorithm based on minimum envelope entropy principle, resulting in a multi-fault feature vector set from 13 time-domain features in the intrinsic mode function (IMF) optimal component of wind turbine gearbox vibration data. Additionally, a fault diagnosis model WOA-CNN-BiLSTM is proposed based on whale optimization algorithm (WOA) and convolutional neural network-bidirectional long-short-term-memory (CNN-BiLSTM), which demonstrates improved fault classification accuracy to 98.3333% and diagnosis accuracy to 98.3853% under conditions of insufficient data when compared with other models.

Data-driven multivariate time series prediction of in-vehicle equipment failure rates

Effectively predicting the failure rate of train-controlled on-board equipment is of great significance for rationally allocating equipment spares, drawing up maintenance plans, and reducing the occurrence of failures. In order to tackle the problem of the intricate attributes and limited predictive precision of the sample data pertaining to the failure rate of on-board equipment, in this paper, a multivariate time series prediction model for the failure rate of train-controlled on-board equipment is based on the combination of multivariate variational modal decomposition (MVMD) graph neural network (GNN) and transformer. First, the original failure rate time series, air temperature, humidity and sand and dust time series are modally decomposed using MVMD, and the intrinsic modal functions (IMFs) of each series are obtained; then, the dynamic graph of the GNN network is defined according to the IMFs, and Transformer’s self-attention mechanism is utilised to capture the dynamic graph’s temporal and spatial dependencies. Finally, the failure rate is output through the feed-forward neural network prediction value. Experiments using the historical fault data of CTCS3-300T train-controlled on-board equipment are carried out to confirm the efficacy of the suggested method, and it is contrasted with other conventional machine learning techniques. The outcomes of the experiment show that compared with other train-controlled on-board equipment failure prediction models, the proposed method has a very good superiority, as evidenced by its mean absolute error (MAE) of 0.0489 and root mean square error (RMSE) of 0.0510, which is of certain reference value for equipment operation and maintenance.

Gearbox Fault Diagnosis Based on Adaptive Variational Mode Decomposition–Stationary Wavelet Transform and Ensemble Refined Composite Multiscale Fluctuation Dispersion Entropy

Existing gearbox fault diagnosis methods are prone to noise interference and cannot extract comprehensive fault signals, leading to misdiagnosis or missed diagnosis. This paper proposes a method for gearbox fault diagnosis based on adaptive variational mode decomposition–stationary wavelet transform (AVMD-SWT) and ensemble refined composite multiscale fluctuation dispersion entropy (ERCMFDE). Initially, the kurtosis coefficient and autocorrelation coefficient are presented, and the Intrinsic Mode Functions are denoised through the application of AVMD-SWT. Secondly, the coarse-grained processing method of composite multiscale fluctuation dispersion entropy is extended to encompass three additional approaches: first-order central moment, second-order central moment, and third-order central moment. This enables the comprehensive extraction of feature information from the time series, thereby facilitating the formation of an initial hybrid feature set. Subsequently, recursive feature elimination (RFE) is employed for feature selection. Ultimately, the outcomes of the faults diagnoses are derived through the utilization of a Support Vector Machine with a Sparrow Search Algorithm (SSA-SVM), with the actual faults data collection and analysis conducted on an experimental platform for gearbox fault diagnosis. The experiments demonstrate that the method can accurately identify gearbox faults and achieve a high diagnostic accuracy of 98.78%.

Diagnosis of incipient faults in wind turbine bearings based on ICEEMDAN–IMCKD

AbstractTo address the difficulty in extracting early fault feature signals of rolling bearings, this paper proposes a novel weak fault diagnosis method for rolling bearings. This method combines the Improved Complementary Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and the Improved Maximum Correlated Kurtosis Deconvolution (IMCKD). Utilizing the kurtosis criterion, the intrinsic mode functions obtained through ICEEMDAN are reconstructed and denoised using IMCKD, which significantly reduces noise in the measured signal. This approach maximizes the energy amplitude at the fault characteristic frequency, facilitating fault feature identification. Experimental studies on two test benches demonstrate that this method effectively reduces noise interference and highlights the fault frequency components. Compared with traditional methods, it significantly improves the signal‐to‐noise ratio and more accurately identifies fault features, meeting the requirements for discriminating rolling bearing faults. The method proposed in this study was applied to the measured vibration signals of the gearbox bearings in the new high‐speed wire department of a Long Products Mill. It successfully extracted weak characteristic information of early bearing faults, achieving the expected diagnostic results. This further validates the effectiveness of the ICEEMDAN–IMCKD method in practical engineering applications, demonstrating significant engineering value for detecting and extracting weak impact characteristics in rolling bearings.

Design of EEG based thought identification system using EMD & deep neural network

Biological communication system for neurological disorder patients is similar to the Brain Computer Interface in a way that it facilitates the connection to the outside world in real time. The interdisciplinary field of Electroencephalogram based message depiction is gaining importance as it assists the paralysed person to communicate. In the proposed method a novel approach of feature extraction is done by Empirical Mode Decomposition on non- stationary & non-linear kind of EEG signal. EMD helps in the effective time frequency analysis by disintegrating the EEG signal in the form of six Intrinsic Mode Functions with help of the frequency components. In all nine features are extracted from the decomposed IMFs so as to predict the states or messages of the patient. The above computed features are then served to the Deep Neural Network to perform the classification. The performance of suggested method is studied through applying it to the acquired database generated by the designed hardware as well as also in real time message depiction. The maximum classification accuracy 97% for the acquired database & 85% in real time are obtained respectively by comparative analysis. The command messages generated from the proposed system helps the person suffering from neurological disorder to establish the communication link with the outside world in an efficient way. Thus, the proposed novel method shows better performance in real time message depiction purpose as related to other existing methods.

Diagnosis of faults using a new VMD-WMRA approach, optimized by a new criterion: Industrial application

This paper proposes a new criterion for selecting the optimum number of Intrinsic Mode Functions (IMFs) from vibration signals measured on rotating machines. The criterion is based on calculating the variation of normalized Shannon entropy ([Formula: see text]) between two successive IMFs, enabling the optimization of the number of processed IMFs. The method combines Variational Mode Decomposition (VMD) with Wavelet Multi-Resolution Analysis (WMRA) using the newly introduced criterion. The key steps involve determining the optimal number of IMFs, decomposing the vibration signals using VMD, and applying WMRA to the selected IMFs. Numerical simulations and experimental results demonstrate its effectiveness in identifying various faults, including gear defects, shaft misalignment, insufficient backlash, and belt defects. These latter flaws are the primary cause of the elevated noise levels in the measured signals. Finally, to validate our approach in an industrial setting, we diagnosed a turbofan, which revealed the presence of several typical faults for this type of installation. The proposed approach addresses a critical industry need by increasing fault diagnosis accuracy in noisy environments. Its practical impact stems from its ability to improve early fault detection, which is critical for predictive maintenance strategies aimed at reducing equipment downtime and extending its lifespan.

A hybrid model based on complementary ensemble empirical mode decomposition, sample entropy and long short-term memory neural network for the prediction of time series signals in NPPs

Accurate and reliable predictions are fundamental for the condition monitoring and maintenance of components and systems in nuclear power plants (NPPs). In this work, we propose a hybrid condition prediction approach based on the combination of complementary ensemble empirical mode decomposition (CEEMD), sample entropy (SampEn) and optimized long short-term memory (LSTM) neural network. Firstly, the CEEMD decomposes the time series signals into multiple subsequences called intrinsic mode functions (IMFs), by doing so, the complexity of the time series signals can be reduced, and this facilitates the accurate prediction of the original signals. Then, in order to reduce the calculation cost of prediction models for subsequences, SampEn is used to measure the complexities of the IMFs, and the IMFs whose values of SampEn are lower than the average are aggregated into a new component. Finally, the LSTM with the hyperparameters optimized by the Bayesian optimization algorithm (BOA) is used to perform the prediction of each component. The prediction results of the original signals are reconstructed by synthesizing the predictions of all components. The proposed hybrid prediction model is utilized on the time series signals collected from an NPP. The results obtained show that the proposed approach can capture the characteristics of the signals and has better performance in prediction accuracy than other models.

Rolling bearing fault diagnosis based on acoustic-vibration data fusion and mode decomposition combined with the crested porcupine optimization algorithm

Variational Mode Decomposition (VMD) is extensively utilized in the domain of rotating machinery fault diagnosis. Nevertheless, the reliance on empirical parameter tuning and the limitations inherent in traditional single-signal (either vibration signals or acoustic signals) fault diagnosis methods present substantial challenges. These include incomplete information and high sensitivity to noise. To address these shortcomings, a new method is introduced that integrates multi-modal sensor data and implements an adaptive VMD approach, enhanced through the Crested Porcupine Optimization Algorithm (CPO) to automatically optimize the key parameter. Then, uses optimized VMD to decompose the time series into intrinsic mode functions of different frequencies to capture the multi-scale characteristics of data. Finally, the decomposed acoustic-vibro signal components are fed into the CNN-BiGRU-AT network, which learns the spatio-temporal dependencies to enhance the accuracy of fault classification. The experimental results conducted across diverse high-noise environments demonstrate that this method’s superior noise robustness compared to single-modality sensor approaches， highlighting the method's potential for machinery fault detection in noisy conditions.

Detecting damage on engine mounts using hilbert-huang transform vibration analysis

Engine mounts, which are usually composed of elastomeric materials like rubber that can absorb excessive vibrations, are built to withstand vibration sources from engines. Engine mounts may eventually degrade from extended use. When rubber products age or sustain damage, they may grow harder and crack. Engine mounts need to be maintained regularly to ensure optimal performance. Visual examinations and the detection of excessive vibrations can be used to accomplish this. Vibration sensors are mounted on the engine mount in axial, vertical, and horizontal orientations using a vibration detection technique utilizing the Hilbert-Huang Transform (HHT) methodology. Matlab is used to examine the data that is gathered at three distinct rotational speeds: 750 rpm, 2000 rpm, and 3000 rpm. The HHT approach combines two key components: the Hilbert Transform, which analyzes the time-frequency signal of the first decomposition until only residuals remain, and Empirical Mode Decomposition (EMD), which breaks down the signal into Intrinsic Mode Functions (IMFs). According to test data, a damaged mount had an amplitude of 0.00005212 m/s² and a frequency of 8 Hz. On the other hand, in typical circumstances, the highest frequency was 7 Hz with the same amplitude. Five frequency increases were made in the damaged mount throughout this operation. In the damaged mount, the Hilbert Transform showed a frequency of 2124 Hz with an amplitude of 0.007594 m/s², indicating a significant resonance. This illustrates how the Hilbert-Huang Transform's capacity to handle non-stationary and nonlinear signal forms allows it to detect damage in components efficiently

Noise robust damage detection of laminated composites using multichannel wavelet-enhanced deep learning model

This paper presents a noise-robust damage detection framework for composite structures via a commonly used vibration-based non-destructive testing (NDT) method. Recently, deep learning-based models have shown promising performance in the autonomous damage detection of laminated composites; however, the poor noise robustness of these models has plagued data-driven damage detection. Moreover, none of the existing studies on damage detection in laminated composites focus on noise-robust deep learning models with high generalization ability. Therefore, this study proposes a hybrid deep learning framework called a multi-channel convolutional autoencoder-support vector machine (MC-CAE-SVM) based on empirical mode decomposition (EMD) and correlation analysis for noise-robust damage detection. This framework aims to first decompose the vibrational signal from multiple health states into intrinsic mode functions (IMFs). Secondly, highly correlated IMFs were extracted using correlation analysis to remove noisy IMFs. Finally, these IMFs were transformed into a time-frequency representation using continuous wavelet transform (CWT) and input to the MC-CAE-SVM model for feature learning and damage detection. Additionally, the accuracy and sensitivity of the model to damage are enhanced by optimizing the MC-CAE-SVM model hyperparameters. Moreover, anti-noise analysis is performed to check the noise-robustness of the proposed model by incorporating noise at various levels. The results showed that the proposed model can provide better damage detection performance compared to conventional models with excellent noise robustness.

Financial Time Series Forecasting Based on Long-Short Term Memory, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Batch Normalization

Long-short term memory (LSTM) is a state-of-art and widely used model to forecast financial time series. However, primitive LSTM networks do not perform well due to over-fitting problems of the deep learning model and nonlinear and non-stationary characteristics of financial time series data. In addition, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is an outstanding data frequency decomposition technique that can decompose original time series into several intrinsic mode functions and a residue. Thus, this paper proposed a novel hybrid network CEEMDAN-LSTM-BN based on LSTM. Specifically, to avoid over-fitting, the modified LSTM-BN network consists of two LSTM layers, two Batch Normalization (BN) layers following each LSTM layer, and a dropout layer. Each of the intrinsic mode functions and the residue would be processed by CEEMDAN-LSTM-BN and the final prediction results are obtained by reconstructing each predictive series. The advantages of the proposed CEEMDANLSTM-BN networks are verified by comparing them to primitive LSTM, other hybrid models, and some famous machine learning models. Moreover, the robustness of the networks is assessed by numerical experiments on different stock indices datasets.

A River Water Quality Prediction Method Based on Dual Signal Decomposition and Deep Learning

Traditional single prediction models struggle to address the complexity and nonlinear changes in water quality forecasting. To address this challenge, this study proposed a coupled prediction model (RF-TVSV-SCL). The model includes Random Forest (RF) feature selection, dual signal decomposition (Time-Varying Filtered Empirical Mode Decomposition, TVF-EMD, and Sparrow Search Algorithm-Optimized Variational Mode Decomposition, SSA-VMD), and a deep learning predictive model (Sparrow Search Algorithm-Convolutional Neural Network-Long Short-Term Memory, SSA-CNN-LSTM). Firstly, the RF method was used for feature selection to extract important features relevant to water quality prediction. Then, TVF-EMD was employed for preliminary decomposition of the water quality data, followed by a secondary decomposition of complex Intrinsic Mode Function (IMF) components using SSA-VMD. Finally, the SSA-CNN-LSTM model was utilized to predict the processed data. This model was evaluated for predicting total phosphorus (TP), total nitrogen (TN), ammonia nitrogen (NH3-N), dissolved oxygen (DO), permanganate index (CODMn), conductivity (EC), and turbidity (TB), across 1, 3, 5, and 7-d forecast periods. The model performed exceptionally well in short-term predictions, particularly within the 1–3 d range. For 1-, 3-, 5-, and 7-d forecasts, R2 ranged from 0.93–0.96, 0.79–0.87, 0.63–0.72, and 0.56–0.64, respectively, significantly outperforming other comparison models. The RF-TVSV-SCL model demonstrates excellent predictive capability and generalization ability, providing robust technical support for water quality forecasting and pollution prevention.

A Deep Learning PM2.5 Hybrid Prediction Model Based on Clustering–Secondary Decomposition Strategy

Accurate prediction of PM2.5 concentration is important for pollution control, public health, and ecological protection. However, due to the nonlinear nature of PM2.5 data, the accuracy of existing methods suffers and performs poorly in both short-term and long-term predictions. In this study, a deep learning hybrid prediction model based on clustering and quadratic decomposition is proposed. The model utilizes the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) to decompose the PM2.5 sequences into multiple intrinsic modal function components (IMFs), and clusters and re-fuses the subsequences with similar complexity by permutation entropy (PE) and K-means clustering. For the fused high-frequency sequences, a secondary decomposition is performed using the whale optimization algorithm (WOA) optimized variational modal decomposition (VMD). Finally, the nonlinear and temporal features are captured for prediction using the long- and short-term memory neural network (LSTM). Experiments show that this proposed model exhibits good stability and generalization ability. It does not only make accurate predictions in the short term, but also captures the trends in the long-term prediction. There is a significant performance improvement over the baseline models. Further comparisons with existing models outperform the current state-of-the-art models.